Is the summation of consistent heuristic functions also consistent?
No, it will not necessary be consistent or admissible. Consider this example, where $s$ is the start, $g$ is the goal, and the distance between them is 1.


s --1-- g


Assume that $h_0$ and $h_1$ are perfect heuristics. Then $h_0(s) = 1$ and $h_1(s) = 1$. In this case the heuristic is inadmissible because $h_0(s)+h_1(s) = 2 &gt; d(s, g)$. Similarly, as an undirected graph the heuristic will be inconsistent because $|h(s)-h(g)| &gt; d(s, g)$.

If you'd like to understand the conditions for the sum of heuristics to be consistent and admissible, I would look at the work on additive PDB heuristics.